A and B can do a work in 45 days and 40 days respectively. They started working together but A left after some days and B alone completed the remaining work in 23 days. After how many days did A leave?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9
Take the whole work as 360 units, the LCM of 45 and 40, so that each person’s daily work is a whole number. B works all the time, so the work B did alone is taken away first; what is left was done by A and B together.
A’s work per day: \(360\div45=8\) units
B’s work per day: \(360\div40=9\) units
Work B did alone in the last 23 days: \(23\times9=207\) units
Work done by A and B together: \(360-207=153\) units
A and B together do \(8+9=17\) units a day, so they worked together for \(153\div17=9\) days
A left after 9 days.